Cyclic Turbulence
8 states, threshold 2 — a higher bar to change
Fewer states and a stricter threshold than the spiral rule, which breaks the wavefronts up into churning, eddy-like domains.
How it works
In plain English, before the notation
The same cyclic idea as the spiral rule, with eight states instead of fourteen, all eight surrounding cells as neighbours instead of four, and — the change that matters most — a cell now needs two neighbours in the next state before it will change, not one. A single advancing cell can no longer drag its neighbours along, so clean wavefronts cannot form and the grid stays in a churning, unsettled state instead.
Compare thresholds side by side
- Open Presets and load "Cyclic Turbulence", then press Play and let it run for 500 steps.
- Now switch to the Belousov–Zhabotinsky rule and run the same length of time.
- The two also differ in state count and neighbourhood, but the threshold is what decides whether you get spirals or churn.
Starting configurations
Loads straight into the simulatorTry any rule
The catalogue covers a few dozen rules. Here you can run any of the 262,144 two-state grid rules, or any of the 256 one-dimensional rules, including ones nobody has written up.
Well-known rules
Where it came from
Threshold variants of cyclic cellular automata were studied by Fisch, Gravner and Griffeath, who mapped out which combinations of state count, threshold and range produce spirals and which do not. This rule sits on the side of that map where spirals fail to form.
The rule, precisely
What each cell looks at
8 neighbours at range 1
What a cell can be
States 0 to 7, arranged in a cycle
The update
next = (k + 1) mod 8 if at least 2 neighbours are in state (k + 1) mod 8; otherwise k
Three parameters again: 8 states, threshold 2, range 1. Raising the threshold makes changes harder to propagate and suppresses the wave behaviour that produces spirals.
Churn instead of structure
The higher threshold changes the outcome qualitatively, not just cosmetically:
- Domains form and dissolve continuously rather than organising into stable rotating cores.
- Boundaries between regions are ragged, because a single cell cannot carry a change forward on its own.
- The pattern never settles into a repeating structure, which makes it a good demonstration that self-organisation is not automatic.
- Fewer states means the cycle completes faster, so the whole thing moves more quickly than the 14-state rule.
Not applicable
Studied as a parameter comparison, not as a computational substrate.
Failure to organise
The useful lesson is negative: a system with the same ingredients as one that self-organises will not necessarily do so. A single parameter can decide the outcome, which is why comparisons like this one are worth running.
Things to try
- Run it next to the spiral rule at the same cell scale and speed — the comparison is the point of this rule.
- Try painting a large uniform block. In the spiral rule it will get eaten from the edges; here it survives much longer.
- Higher speeds suit this rule, since nothing settles anyway.